Background: SARS-CoV-2 has caused a global pandemic since early 2020 and remains a serious public health issue worldwide. Four structural genes, envelope (E), membrane (M), nucleocapsid (N) and spike (S), play a key role in controlling entry into human cells and virion assembly of SARS-CoV-2. The evolution of these genes may determine infectivity of SARS-CoV-2, but thus far, little is known about them. Methods: We analyzed 3090 SARS-CoV-2 isolates from the GenBank database to determine the evolutionary patterns of the four structural genes by employing various molecular evolution algorithms. Results: Phylogenetic analyses showed that global SARS-CoV-2 isolates can be clustered into three to four major clades based upon protein sequence. Although intragenic recombination was not detected among different alleles, purifying selection has affected the evolution of these genes. By analyzing full genomic sequences of these alleles, our result revealed that codon 614 of the S glycoprotein has been subjected to a strong positive selection pressure, and a consistent D614G mutation was identified. Additionally, another potentially positive selection site at codon 5 in the signal sequence of the S protein was also identified with a consistent L5F mutation. The allele containing the D614G mutation has undergone significant expansion during SARS-CoV-2 transmission, implying a better adaptability of isolates with the mutation. Nevertheless, L5F allele expansion was found to be relatively restricted. The D614G mutation is located at subdomain 2 (SD2) of the C-terminal portion (CTP) of the S1 subunit. Protein structural modeling showed that the D614G mutation may cause the disruption of a salt bridge between S protein monomers and increase their flexibility, consequently promoting receptor binding domain (RBD) opening, virus attachment, and ultimately entry into host cells. Located at the signal sequence of S protein, the L5F mutation may facilitate protein folding, assembly, and secretion of the virus. Conclusions: This is the first reported evidence of positive Darwinian selection in the spike gene of SARS-CoV-2. This finding contributes to a broader understanding of the adaptive mechanisms of this virus, and provide insight for the development of novel therapeutic approaches, as well as the creation of effective vaccines, through targeting mutation sites.